Complex conjugate matrix equations for systems and control
The book is the first book on complex matrix equations including the conjugate of unknown matrices. The study of these conjugate matrix equations is motivated by the investigations on stabilization and model reference tracking control for discrete-time antilinear systems, which are a particular kind...
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| Main Authors | , |
|---|---|
| Format | Electronic eBook |
| Language | English |
| Published |
Singapore :
Springer,
2016.
|
| Series | Communications and control engineering.
|
| Subjects | |
| Online Access | Full text |
| ISBN | 9789811006371 9789811006357 |
| ISSN | 0178-5354 |
| Physical Description | 1 online resource (xviii, 487 pages) : illustrations |
Cover
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| 100 | 1 | |a Wu, Ai-Guo, |e author. | |
| 245 | 1 | 0 | |a Complex conjugate matrix equations for systems and control / |c Ai-Guo Wu, Ying Zhang. |
| 264 | 1 | |a Singapore : |b Springer, |c 2016. | |
| 264 | 4 | |c ©2017 | |
| 300 | |a 1 online resource (xviii, 487 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a počítač |b c |2 rdamedia | ||
| 338 | |a online zdroj |b cr |2 rdacarrier | ||
| 490 | 1 | |a Communications and control engineering, |x 0178-5354 | |
| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | |a Preface; Contents; Notation; 1 Introduction; 1.1 Linear Equations; 1.2 Univariate Linear Matrix Equations; 1.2.1 Lyapunov Matrix Equations; 1.2.2 Kalman-Yakubovich and Normal Sylvester Matrix Equations; 1.2.3 Other Matrix Equations; 1.3 Multivariate Linear Matrix Equations; 1.3.1 Roth Matrix Equations; 1.3.2 First-Order Generalized Sylvester Matrix Equations; 1.3.3 Second-Order Generalized Sylvester Matrix Equations; 1.3.4 High-Order Generalized Sylvester Matrix Equations; 1.3.5 Linear Matrix Equations with More Than Two Unknowns; 1.4 Coupled Linear Matrix Equations. | |
| 505 | 8 | |a 1.5 Complex Conjugate Matrix Equations1.6 Overview of This Monograph; 2 Mathematical Preliminaries; 2.1 Kronecker Products; 2.2 Leverrier Algorithms; 2.3 Generalized Leverrier Algorithms; 2.4 Singular Value Decompositions; 2.5 Vector Norms and Operator Norms; 2.5.1 Vector Norms; 2.5.2 Operator Norms; 2.6 A Real Representation of a Complex Matrix; 2.6.1 Basic Properties; 2.6.2 Proof of Theorem 2.7; 2.7 Consimilarity; 2.8 Real Linear Spaces and Real Linear Mappings; 2.8.1 Real Linear Spaces; 2.8.2 Real Linear Mappings; 2.9 Real Inner Product Spaces; 2.10 Optimization in Complex Domain. | |
| 505 | 8 | |a 2.11 Notes and ReferencesPart I Iterative Solutions; 3 Smith-Type Iterative Approaches; 3.1 Infinite Series Form of the Unique Solution; 3.2 Smith Iterations; 3.3 Smith (l) Iterations; 3.4 Smith Accelerative Iterations; 3.5 An Illustrative Example; 3.6 Notes and References; 4 Hierarchical-Update-Based Iterative Approaches; 4.1 Extended Con-Sylvester Matrix Equations; 4.1.1 The Matrix Equation AXB+CoverlineXD=F; 4.1.2 A General Case; 4.1.3 Numerical Examples; 4.2 Coupled Con-Sylvester Matrix Equations; 4.2.1 Iterative Algorithms; 4.2.2 Convergence Analysis; 4.2.3 A More General Case. | |
| 505 | 8 | |a 4.2.4 A Numerical Example4.3 Complex Conjugate Matrix Equations with Transpose of Unknowns; 4.3.1 Convergence Analysis; 4.3.2 A Numerical Example; 4.4 Notes and References; 5 Finite Iterative Approaches; 5.1 Generalized Con-Sylvester Matrix Equations; 5.1.1 Main Results; 5.1.2 Some Special Cases; 5.1.3 Numerical Examples; 5.2 Extended Con-Sylvester Matrix Equations; 5.2.1 The Matrix Equation AXB+CoverlineXD=F; 5.2.2 A General Case; 5.2.3 Numerical Examples; 5.3 Coupled Con-Sylvester Matrix Equations; 5.3.1 Iterative Algorithms; 5.3.2 Convergence Analysis; 5.3.3 A More General Case. | |
| 505 | 8 | |a 5.3.4 Numerical Examples5.3.5 Proofs of Lemmas 5.15 and 5.16; 5.4 Notes and References; Part II Explicit Solutions; 6 Real-Representation-Based Approaches; 6.1 Normal Con-Sylvester Matrix Equations; 6.1.1 Solvability Conditions; 6.1.2 Uniqueness Conditions; 6.1.3 Solutions; 6.2 Con-Kalman-Yakubovich Matrix Equations; 6.2.1 Solvability Conditions; 6.2.2 Solutions; 6.3 Con-Sylvester Matrix Equations; 6.4 Con-Yakubovich Matrix Equations; 6.5 Extended Con-Sylvester Matrix Equations; 6.6 Generalized Con-Sylvester Matrix Equations; 6.7 Notes and References; 7 Polynomial-Matrix-Based Approaches. | |
| 506 | |a Plný text je dostupný pouze z IP adres počítačů Univerzity Tomáše Bati ve Zlíně nebo vzdáleným přístupem pro zaměstnance a studenty | ||
| 520 | |a The book is the first book on complex matrix equations including the conjugate of unknown matrices. The study of these conjugate matrix equations is motivated by the investigations on stabilization and model reference tracking control for discrete-time antilinear systems, which are a particular kind of complex system with structure constraints. It proposes useful approaches to obtain iterative solutions or explicit solutions for several types of complex conjugate matrix equation. It observes that there are some significant differences between the real/complex matrix equations and the complex conjugate matrix equations. For example, the solvability of a real Sylvester matrix equation can be characterized by matrix similarity; however, the solvability of the con-Sylvester matrix equation in complex conjugate form is related to the concept of con-similarity. In addition, the new concept of conjugate product for complex polynomial matrices is also proposed in order to establish a unified approach for solving a type of complex matrix equation. | ||
| 590 | |a SpringerLink |b Springer Complete eBooks | ||
| 650 | 0 | |a Matrices. | |
| 655 | 7 | |a elektronické knihy |7 fd186907 |2 czenas | |
| 655 | 9 | |a electronic books |2 eczenas | |
| 700 | 1 | |a Zhang, Ying, |e author. | |
| 776 | 0 | 8 | |i Erscheint auch als: |n Druck-Ausgabe |t Wu, Ai-Guo. Complex Conjugate Matrix Equations for Systems and Control |
| 830 | 0 | |a Communications and control engineering. | |
| 856 | 4 | 0 | |u https://proxy.k.utb.cz/login?url=https://link.springer.com/10.1007/978-981-10-0637-1 |
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